概率论一道题,求教Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability
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![概率论一道题,求教Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability](/uploads/image/z/3816179-35-9.jpg?t=%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%80%E9%81%93%E9%A2%98%2C%E6%B1%82%E6%95%99Do+you+have+a+rare+disease%3FSuppose+that+1+in+633+people+have+a+particular+disease.You+go+to+the+doctor+and+they+suggest+that+you+be+tested+for+the+disease.The+test+will+accurately+give+a+positive+test+result+with+probability)
概率论一道题,求教Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability
概率论一道题,求教
Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability 0.94,and will accurately give a negative test result with probability 0.81.If the test comes back positive,what is the probability you have the disease?
概率论一道题,求教Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability
A1表示患病,A2表示无病 ,B表示检查阳性
根据贝叶斯公式和全概公式,所求条件概率P(A1|B)=P(B|A1)P(A1)/[P(B|A1)P(A1)+P(B|A2)P(A2)]=(1/633 *0.94)/(1/633* 0.94 + 632/633 *0.19) =47/605 约为0.0078(由于无病误诊为阳性的概率0.19太高导致结果极不可信)